Panu Pekko

Determination of doping and temperature-dependent elastic constants of degenerately doped silicon from MEMS resonators

Elastic constants c₁₁, c₁₂, and c₄₄ of degenerately doped silicon are studied experimentally as a function of the doping level and temperature. First-and second-order temperature coefficients of the elastic constants are extracted from measured resonance frequencies of a set of MEMS resonators fabricated on seven different wafers doped with phosphorus (carrier concentrations 4.1, 4.7, and 7.5 × 10¹⁹ cm^-3), arsenic (1.7 and 2.5 × 10¹⁹ cm^-3), or boron (0.6 and 3 × 10¹⁹ cm^-3). Measurements cover a temperature range from -40°C to +85°C. It is found that the linear temperature coefficient of the shear elastic parameter c₁₁ - c₁₂ is zero at n-type doping level of n ~ 2 × 10¹⁹ cm^-3, and that it increases to more than 40 ppm/K with increasing doping. This observation implies that the frequency of many types of resonance modes, including extensional bulk modes and flexural modes, can be temperature compensated to first order. The second-order temperature coefficient of c₁₁ - c₁₂ is found to decrease by 40% in magnitude when n-type doping is increased from 4.1 to 7.5 × 10¹⁹ cm^-3. Results of this study enable calculation of the frequency drift of an arbitrary silicon resonator design with an accuracy of ±25 ppm between the calculated and real(ized) values over T = -40°C to +85°C at the doping levels covered in this work. Absolute frequency can be estimated with an accuracy of ±1000 ppm.

Optimized design and process for making a DC voltage reference based on MEMS

A micromechanical moving plate capacitor has been designed and fabricated for use as a dc voltage reference. The reference is based on the characteristic pull-in property of a capacitive microelectromechanical system (MEMS) component. The design is optimized for stability. A new silicon-on-insulator (SOI) process has been developed to manufacture the component. We also report on improved feedback electronics and the latest measurement results.

Plug-up-a new concept for fabricating SOI MEMS devices

This paper reports a novel process sequence for fabricating micromechanical devices on silicon-on-insulator (SOI) wafers. Among the merits of the described process are its improved immunity to stiction and elimination of conductor metal endurance problems during sacrificial etching in hydrofluoric acid. With this novel process one can controllably embed vacuum cavities within SOI substrates. Further processing of such cavity wafers enables realization of a wide variety of micromechanical devices based on single crystalline silicon or even integrated read-out circuitry.

High-Q micromechanical resonators for mass sensing in dissipative media

Single crystal silicon-based micromechanical resonators are developed for mass sensing in dissipative media. The design aspects and preliminary characterization of the resonators are presented. For the suggested designs, quality factors of about 20 000 are typically measured in air at atmospheric pressure and 1000–2000 in contact with liquid. The performance is based on a wine-glass-type lateral bulk acoustic mode excited in a rectangular resonator plate. The mode essentially eliminates the radiation of acoustic energy into the sample media leaving viscous drag as the dominant fluid-based dissipation mechanism in the system. For a mass loading distributed over the central areas of the resonator a sensitivity of 27 ppm ng−1 is measured exhibiting good agreement with the results of the finite element method-based simulations. It is also shown that the mass sensitivity can be somewhat enhanced, not only by the proper distribution of the loaded mass, but also by introducing shallow barrier structures on the resonator.

Wideband Microwave Power Sensor Based on MEMS Technology

An optimized transmission-type MEMS RF power sensor is presented. The design is based on microwave filter theory. It is shown that the thermal resolution of the sensor can be reduced below -50 dBm for RF bandwidths up to les 40 GHz

Low-temperature processes for MEMS device fabrication

The high temperatures typical in semiconductor and conventional MEMS fabrication limit the material choices in MEMS structures. This paper reviews some of the low-temperature processes and techniques available for MEMS fabrication and describes some characteristics of these techniques and practical process examples. The techniques described are plasma-enhanced chemical vapour deposition, atomic layer deposition, reactive sputtering, vapour phase hydrofluoric acid etching of low-temperature oxides, and low-temperature wafer bonding. As a practical example of the use of these techniques, the basic characteristics of a MEMS switch and other devices fabricated at VTT are presented.

Experimental Determination of the Temperature Dependency of the Elastic Constants of Degenerately Doped Silicon

We study experimentally the temperature dependence of the elastic constants of degenerately doped silicon as a function of the doping level. First and second order thermal coefficients of the elastic constants are extracted from the temperature dependent resonance frequencies of a set of MEMS resonators fabricated on phosphorus, arsenic and boron doped wafers having maximum doping levels of 7.5 × 10¹⁹cm ^-3, 2.5 × 10¹⁹cm ^-3 and 3 × 10¹⁹cm ^-3, respectively. Trends in the behavior of the thermal coefficients as a function of doping are identified and discussed.

Design Rules for Temperature Compensated Degenerately n-Type-Doped Silicon MEMS Resonators

The first- and second-order temperature coefficients and the total temperature-induced frequency deviation of degenerately n-type-doped silicon resonators are modeled. Modeling is based on finite element modelling-based sensitivity analysis of various resonator geometries combined with the experimental results on doping-dependent elastic constants of n-type-doped silicon. The analysis covers a doping range from 2.4 × 1017 to 7.5 × 1019 cm-3. Families of resonance modes that can be temperature compensated via n-type doping are identified. These include bulk modes, such as the width/length extensional modes of a beam, Lamé/square extensional modes of a plate resonator, as well as flexural and torsional resonance modes. It is shown that virtually all resonance modes of practical importance can reach zero linear temperature coefficient of frequency when correctly designed. Optimal configurations are presented, where a total frequency deviation of ~150 ppm can be reached. The results suggest that full second-order temperature compensation familiar from AT cut quartz is not possible in silicon resonators with doping below 7.5 × 1019 cm-3. However, an analysis relying on extrapolated elastic constant data suggests the possibility of full second-order temperature compensation for a wide range of resonance modes when doping is extended beyond 1020 cm-3.

Second order temperature compensated piezoelectrically driven 23 MHz heavily doped silicon resonators with ±10 ppm temperature stability

We report quartz level temperature stability of piezoelectrically driven silicon MEMS resonators. Frequency stability of better than ±10 ppm is measured for 23 MHz extensional mode resonators over a temperature range of T = -40 ... + 85°C. The temperature compensation mechanism is entirely passive, relying on the tailored elastic properties of heavily doped silicon with a doping level of n > 1020cm-3, and on an optimized resonator geometry. The result highlights the potential of silicon MEMS resonators to function as pin-to-pin compatible replacements for quartz crystals without any active temperature compensation.

Long term stability and quality factors of degenerately n-type doped silicon resonators

Effect of degenerate doping on the long term stability and quality factors of silicon resonators was studied. The long term stability of electrostatically coupled tuning fork and width extensional mode resonators was found to be better than 1 ppm during a measurement spanning 220 days. Resonators were phosphorus doped to a carrier concentration of 4.1×1019cm-3. Quality factors of ~10-MHz Lamé mode resonators on wafers doped up to a concentration of 7.5 × 1019cm-3 were found to range from 900,000 to 1,500,000, which is comparable to that reported for similar resonators with moderate doping. The results indicate that the effect from heavy phosphorus doping on resonator stability or on silicon intrinsic losses is low at the studied doping levels.